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Question

The point having position vectors 2i + 3j + 4k, 3i + 4j + 2k, 4i + 2j + 3k are the vertices of.

A
Right angled triangle
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B
Equilateral triangle
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C
Isosceles triangle
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D
Collinear
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Solution

The correct option is B Equilateral triangle
a=2i+3j+4k,
b=3i+4j+2k,
c=4i+2j+3k,
a.b=(2i+3j+4k).(3i+4j+2k)
=6+12+8
=26
b.c=(3i+4j+2k).(4i+2j+3k)
=12+8+6
=26
c.a=(4i+2j+3k).(2i+3j+4k)
=8+6+12
=26
Hence, Since a.b=b.c=c.a
So it is an Equilateral triangle

1139277_426424_ans_f40f03b592b14ae191f8abb0310defef.png

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